Abstract
Real-valued implication (R-implication) is a Boolean consistent generalization of the classical binary implication. R-implication plays important roles in real-valued set (R-set) theory as a generalization of classical set theory as well as in many applications such as morphology in image processing, association rules in data mining and decision making generally.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baczynski, M., Jayaram, B.: Fuzzy Implications. STUDFUZZ. Springer (2008)
Radojevic, D.: There is Enough Room for Zadeh’s Ideas, besides Aristotle’s in Boolean Frame. In: IEEE SOFA 2007, Szeged - Hungary, Arad – Rumania, pp. 79–83 (2007)
Radojevic, D.: Interpolative Realization of Boolean Algebra as a Consistent Frame for Gradation and/or Fuzziness. In: Nikravesh, M., Kacprzyk, J., Zadeh, L.A. (eds.) Forging New Frontiers: Fuzzy Pioneers II, December 2007. STUDFUZZ, pp. 295–318. Springer (2007)
Radojevic, D.: Real sets as consistent Boolean generalization of classical sets. In: Zadeh, L.A., Tufis, D., Filip, F.G., Dzitac, I. (eds.) From Natural Language to Soft Computing: New Paradigms in Artificial Intelligence, pp. 150–171. Editing House of Romanian Academy (2009) ISBN: 978-973-27-1678-6
Shi, Y., van Gasse, B., Ruan, D., Kerre, E.: Axioms for fuzzy implications: dependence and independence. In: 30th Linz Seminar on Fuzzy Set Theory, Abstracts, Linz 2009, pp. 104–105 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Radojević, D.G. (2013). Real-Valued Implication as Generalized Boolean Polynomial. In: Balas, V., Fodor, J., Várkonyi-Kóczy, A. (eds) New Concepts and Applications in Soft Computing. Studies in Computational Intelligence, vol 417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28959-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-28959-0_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28958-3
Online ISBN: 978-3-642-28959-0
eBook Packages: EngineeringEngineering (R0)